Method Of Estimating A Subterranean Formation Property

Abstract

A method of analyzing a subterranean formation may include collecting a plurality of tool responses from different tools and generating a respective theoretical equation relating tool responses for each of the tools to properties of the subterranean formation. The method may also include generating a database having the tool responses stored therein based upon each respective theoretical equation and generating a non-linear mapping function relating at least one of the tool responses to at least one property of the subterranean formation. The method may also include estimating a value for the at least one property based upon the non-linear mapping function.

That which is claimed is: 
     
         1 . A method of analyzing a subterranean formation comprising:
 collecting a plurality of tool responses from a plurality of different tools;   generating a respective theoretical equation relating tool responses for each of the tools to a plurality of properties of the subterranean formation;   generating a database having the tool responses stored therein based upon each respective theoretical equation;   generating a non-linear mapping function relating at least one of the tool responses to at least one property of the subterranean formation; and   estimating a value for the at least one property based upon the non-linear mapping function.   
     
     
         2 . The method of  claim 1 , wherein the database is generated by at least varying ones of the plurality of properties of the subterranean formation to be estimated over an expected range of values. 
     
     
         3 . The method of  claim 1 , wherein the value is estimated to be consistent with the respective theoretical equation. 
     
     
         4 . The method of  claim 1 , wherein the value is estimated to be consistent with at least one of the tool responses. 
     
     
         5 . The method of  claim 1 , wherein the non-linear mapping function comprises at least one radial basis function. 
     
     
         6 . The method of  claim 5 , wherein the at least one radial basis function comprises at least one Gaussian radial basis function. 
     
     
         7 . The method of  claim 6 , wherein a width of the at least one Gaussian radial basis function is determined based upon adjacent ones of the tool responses stored in the database. 
     
     
         8 . The method of  claim 1 , wherein a coefficient of the non-linear mapping function is generated non-iteratively based upon the database. 
     
     
         9 . The method of  claim 1 , further comprising displaying at least some of the tool responses stored in the database in a plurality of dimensions for the at least one property. 
     
     
         10 . A method of analyzing a subterranean formation comprising:
 collecting a plurality of tool responses from a plurality of different tools;   generating a respective theoretical equation relating tool responses for each of the tools to a plurality of properties of the subterranean formation;   generating a database having the tool responses stored therein based upon each respective theoretical equation by at least varying ones of the plurality of properties of the subterranean formation to be estimated over an expected range of values;   generating a non-linear mapping function comprising at least one radial basis function relating at least one of the tool responses to at least one property of the subterranean formation; and   estimating a value for the at least one property based upon the non-linear mapping function.   
     
     
         11 . The method of  claim 10 , wherein the value is estimated to be consistent with the respective theoretical equation. 
     
     
         12 . The method of  claim 10 , wherein the value is estimated to be consistent with at least one of the tool responses. 
     
     
         13 . The method of  claim 10 , wherein the at least one radial basis function comprises a Gaussian radial basis function. 
     
     
         14 . The method of  claim 10 , wherein a coefficient of the non-linear mapping function is generated non-iteratively based upon the database. 
     
     
         15 . A non-transitory computer-readable medium for analyzing a subterranean formation, the non-transitory computer-readable medium having computer-executable instructions for:
 collecting a plurality of tool responses from a plurality of different tools;   generating a respective theoretical equation relating tool responses for each of the tools to a plurality of properties of the subterranean formation;   generating a database having the tool responses stored therein based upon each respective theoretical equation;   generating a non-linear mapping function relating at least one of the tool responses to at least one property of the subterranean formation; and   estimating a value for the at least one property based upon the non-linear mapping function.   
     
     
         16 . The non-transitory computer-readable medium of  claim 15 , wherein the computer-executable instructions are for generating the database by at least varying ones of the subterranean formation properties to be estimated over an expected range of values. 
     
     
         17 . The non-transitory computer-readable medium of  claim 15 , wherein the computer-executable instructions are for estimating the value estimated to be consistent with the respective theoretical equation. 
     
     
         18 . The non-transitory computer-readable medium of  claim 15 , wherein the computer-executable instructions are for estimating the value to be consistent with at least one of the tool responses. 
     
     
         19 . The non-transitory computer-readable medium of  claim 15 , wherein the computer-executable instructions are for generating a non-linear mapping function comprising at least one Gaussian radial basis function. 
     
     
         20 . The non-transitory computer-readable medium of  claim 19 , wherein the at least one radial basis function comprises at least one Gaussian radial basis function. 
     
     
         21 . The non-transitory computer-readable medium of  claim 15 , wherein the computer-executable instructions are for generating a coefficient of the non-linear mapping function non-iteratively based upon the database. 
     
     
         22 . The non-transitory computer-readable medium of  claim 15 , wherein the computer-executable instructions are for displaying at least some of the tool responses stored in the database in a plurality of dimensions for the at least one property.